Compensating for time varying phase changes in interferometric measurements

ABSTRACT

An optical device under test (DUT) is interferometrically measured. The DUT can include one or more of an optical fiber, an optical component, or an optical system. First interference pattern data for the DUT is obtained for a first path to the DUT, and second interference pattern data for the DUT is obtained for a second somewhat longer path to the DUT. Because of that longer length, the second interference pattern data is delayed in time from the first interference pattern data. A time varying component of the DUT interference pattern data is then identified from the first and second interference pattern data. The identified time varying component is used to modify the first or the second interference pattern data to compensate for the time-varying phase caused by vibrations, etc. One or more optical characteristics of the DUT may then be determined based on the modified interference pattern data.

This application is a divisional application of U.S. application Ser.No. 11/792,082, which is the U.S. national phase of internationalapplication PCT/US2005/045002 filed 13 Dec. 2005, which designated theU.S. and claims priority from U.S. Provisional Patent Application No.60/635,440, filed on Dec. 14, 2004 and from U.S. Provisional PatentApplication No. 60/659,866, filed on Mar. 10, 2005, the entire contentsof each of which are incorporated by reference.

RELATED PATENT APPLICATION

This application is related to commonly-assigned U.S. patent applicationSer. No. 11/062,740, filed on Feb. 23, 2005, the contents of which areincorporated by reference.

TECHNICAL FIELD

The technical field relates to measurement equipment and techniques, andmore particularly, to improving the accuracy, precision, and applicationof interferometric measurements. One non-limiting example application isOptical Frequency Domain Reflectometry (OFDR).

BACKGROUND AND SUMMARY

Mixing between a reference signal and a data signal is often necessaryto extract information about an optical device or network. A probesignal and a reference signal originating from the same source typicallymix or interfere, resulting in optical interference “fringes.” Apositive fringe occurs when the light is in phase and constructivelycombines (interferes) to a greater intensity, and a negative fringeoccurs when the light is 180 degrees out of phase and destructivelycombines (interferes) to cancel out the light. The fringe intensitiescan be detected and used to assess information about the device beingprobed. In interferometric sensing, a reference signal is mixed with areflected probe signal whose phase and/or amplitude is modified by aparameter to be measured. The mixing produces an interference signal,and the amplitude of the interference signal depends on how efficientlythe two optical signals mix.

Optical Frequency Domain Reflectometry (OFDR) may be used to providedata related to one or more optical characteristics (e.g., backscatter,dispersion, etc.) of a fiber or fiber optic device that is part of afiber over relatively short fiber distances, e.g., less than severalhundred meters, but with relatively high “spatial” resolutions, e.g.,centimeters and less. High spatial resolution is valuable for manyreasons. For example, it allows more precise location and/ordetermination of optical characteristic of “events” like fiber flaws,cracks, strains, temperature changes, etc. and devices like couplers,splitters, etc. High resolution also allows performing such operationswith a level of precision that distinguishes between events or deviceslocated close together. Without that high resolution, measurements forclosely located events or devices cannot be made on an individual eventor device level. For these and other reasons, it would be very desirableto apply OFDR to longer fibers in order to attain this high resolutionalong longer distances.

Unfortunately, there are two major unsolved obstacles to successfullyapplying OFDR to longer fibers. One is dynamic phase changes caused bytime varying changes in the length of the fiber under test. One sourceof those time-varying changes is vibration. As a fiber vibrates, itslength changes causing different time delays in the reflected lighttraversing those different fiber lengths. For OFDR to work well, thephase of the reflected light along the fiber should be static and notvary with time. If the time variance of the phase occurs slowly relativeto the speed with which the interference pattern intensity data isacquired, then the phase changes are not a problem. But if the speedwith which the interference pattern intensity data is detected/acquiredis slower than the speed at which the phase changes, then the phasechanges cannot be ignored.

The speed at which OFDR interference pattern intensity data is acquiredis a function of how fast the tunable laser in the OFDR is “swept” overthe frequency range of interest and the fiber length. There is a limiton how fast tunable lasers can be swept in terms of bandwidth, amplifiercosts, increased power requirements, and processing speed. Regardless oflaser sweep speeds, longer fibers require more time to acquire themeasurement data, and there is much more of that data. That large amountof data is the second obstacle because there are practical constraintson how much data can be efficiently and cost effectively stored andprocessed.

To avoid these obstacles, the inventors discovered how to compensate forthe time-varying phase caused by vibrations and any other cause so thatlaser sweep speed and data set size need not be increased. An opticaldevice under test (DUT) is interferometrically measured. The DUT caninclude one or more of an optical fiber, an optical component, or anoptical system. The DUT can be coupled to the measurement system (e.g.,an OFDR) via optical fiber, via some other medium, or even via freespace. First interference pattern data for the DUT is obtained for afirst path to the DUT, and second interference pattern data is obtainedfor a second somewhat longer path to the DUT. Because of that longerlength, the second interference pattern data is delayed in time from thefirst interference pattern data. A time varying component of the DUTinterference pattern data is then identified from the first and secondinterference pattern data. The identified time varying component is usedto modify the first or the second interference pattern data. One or moreoptical characteristics of the DUT is determined based on the modifiedinterference pattern data. For example, if the DUT includes a fiberhaving a length greater than 500 meters, the modified interferencepattern data may be used to determine one or more opticalcharacteristics at any position along the fiber. Indeed, that positionalong the fiber may be determined with a resolution, for example, of oneor two centimeters based on the modified interference pattern data.

The first and second interference pattern data each include static phaseinformation and dynamic phase information. The time varying componentincludes the dynamic phase information. The first and second fringeinterference pattern data is combined to substantially remove the staticphase information. For example, the first or the second interferencepattern data can be combined to remove the vibration-induced phasechanges that adversely affect the interference pattern data obtained forthe DUT.

A preferred, non-limiting, example is implemented as an OpticalFrequency Domain Reflectometer (OFDR) to obtain the first interferencepattern data and the second interference pattern data. Preferably, thefirst and second interference pattern data is compensated fornon-linearity associated with a tunable laser used in the OFDR to obtaincompensated first and second interference pattern data (compensated forthe affect on the data due to non-linearities in the laser tuning). Oneexample processing approach that can be used by the OFDR includes thefollowing steps: transforming the first and second interference patterndata into the frequency domain, capturing a first window of frequencydomain data for the first interference pattern data corresponding to aportion of the DUT under analysis, capturing a second window offrequency domain data for the second interference pattern datacorresponding to the portion of the DUT under analysis, converting thefirst and second windows of frequency domain data into first and secondcorresponding phase data, and combining the first and secondcorresponding phase data.

Other aspects of this technology includes advantageous methods forprocessing interference pattern data generated by an interferometer. Theinterferometer provides a laser signal from a tunable laser along agiven optical path having an associated path delay and to a referenceoptical path and combines light reflected from the given optical pathand from the reference path, thereby generating the interference patterndata. (The given optical path may be, for example, associated with adevice under test (DUT)). A first laser optical phase of the lasersignal is estimated, and an expected complex response for the givenoptical path is calculated based on the estimated laser optical phase.The interference pattern data from the interferometer is multiplied bythe expected complex response to generate a product. The product isfiltered to extract interference pattern data associated with the givenoptical path from the interference pattern data generated by theinterferometer.

In one non-limiting example implementation, calculating the expectedcomplex response for the given optical path based on the estimated laseroptical phase includes estimating a delayed version of the laser opticalphase of the laser signal, determining a difference phase between thedelayed version of the estimated laser optical phase and the estimatedfirst laser optical phase, calculating the cosine of the differencephase to form the real part of the expected complex response, andcalculating the sine of the difference phase to form the imaginary partof the expected complex response. This expected complex response is thenmultiplied by the interference pattern data. The real and imaginaryparts of the resulting complex signals are low pass filtered anddecimated to extract interference pattern data associated with the givenoptical path from the interference pattern data generated by theinterferometer. Estimating the laser optical phase includes coupling aportion of the laser light to a second interferometer, converting aninterference fringe or pattern signal from the second interferometerinto a digital signal corresponding to the interference pattern data,the digital signal being a sampled form of the interference fringesignal, and estimating the laser phase based upon the digital signal.

A first derivative of the laser optical phase may be estimated based onthe digital signal by Fourier transforming the digital signal, windowingthe transformed signal to identify a portion of the transformed signalthat corresponds to the given optical path delay, inverse Fouriertransforming the windowed signal, and computing the phase of the signal.Equivalently, a second derivative of the laser optical phase may beestimated by identifying zero crossings of the digital signal andcounting a number of samples between the zero crossings of the digitalsignal. Calculating an expected complex response for the given opticalpath based on the estimated laser optical phase may be accomplished byestimating a second derivative of the laser optical phase, calculating arunning sum of the second derivative of the laser optical phase, where alength of the running sum is associated with a length of the givenoptical path delay, accumulating the running sum, calculating a sine ofthe accumulated sum to form the imaginary part of the expected complexresponse, and calculating a cosine of the accumulated sum to form thereal part of the expected complex response. The real and imaginary partsof the expected complex response are low pass filtered and decimated toextract interference pattern data associated with the given optical pathfrom the interference pattern data generated by the interferometer.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a non-limiting example of an OFDR type measurementsystem that compensates for time varying phase changes ininterferometric measurements;

FIG. 2( a) illustrates interference patterns or fringes from a singlereflection where the path is time varying;

FIG. 2( b) illustrates the Fourier transform of pattern and FIG. 2( b);

FIG. 3 illustrates three graphs that plot the phase of the two signalsshown in FIG. 2( a) as a function of time, then the phase differencebetween the two phase measurements, and then the integral of the phasedifference;

FIG. 4 illustrates a second non-limiting example of an OFDR embodiment;

FIG. 5 illustrates a third non-limiting example of an OFDR embodiment;

FIG. 6 is a diagram that illustrates one example approach for achievingpolarization stability issues for long delay lines;

FIG. 7 illustrates one example configuration to provide a morepolarization stable delay lines;

FIG. 8 illustrates a fourth non-limiting example of an OFDR embodiment;

FIG. 9 is a diagram that shows a vibration impacting a fiber DUT;

FIG. 10 illustrates a non-limiting experimental OFDR for testingvibration tolerance;

FIG. 11 is a graph illustrating a Fourier transform of frequencylinearized interference pattern data;

FIG. 12 is a graph of one portion of the graph in FIG. 11;

FIG. 13 is a graph that plots phase as measured by near and farinterferometers;

FIG. 14 is a graph illustrating phase data uncorrected for vibrationrelative to phase corrected phase data;

FIG. 15 is a fifth non-limiting example of an OFDR embodiment;

FIG. 16 is a graph illustrating amplitude signals after being Fouriertransform for the example embodiment from FIG. 17;

FIG. 17 is a diagram illustrating a sixth example of non-limiting OFDRembodiment;

FIG. 18 is an flow diagram of example processing steps for determiningtime varying phase;

FIGS. 21-27 illustrate various delay paths in a example OFDR;

FIG. 28 illustrates windowing function;

FIG. 29 illustrate three graphs related to the amplitude of transformedLM phase;

FIG. 30 is a function block diagram of a digital signal processing blockas an example preferred (but not limiting) implementation for reducingthe data set size, processing time, and memory requirements;

FIG. 31 is a graph of samples as a detected and digitized LM datasignal;

FIG. 32 is graph of an example derivative of the phase as calculatedfrom the signal in FIG. 31;

FIG. 33 is a function block diagram of a digital circuit that may beused to detect rising zero crossings of digitized signals;

FIG. 34 is a function block diagram of a digital circuit that may beused to calculate the phase derivative signal from the rising zerocrossing signal determined in FIG. 33;

FIG. 35 is a graph of an example laser phase correction signal for a LMinterferometer;

FIG. 36 is a graph of the impulse response obtained from a Fouriertransform of the windowed phase correction function shown in FIG. 35;

FIG. 37 is an example shift register for using in determining near andfar phases from LM phase;

FIG. 38 is a graph of the a six-segmented Blackman Windowed Syncfunction;

FIG. 39 is a function block diagram of a decimating six segment digitalfilter;

FIG. 40 is a schematic of a non-limiting example of an optical networkwith a delayed reference path;

FIG. 41 is a graph that illustrates a signal delay DUT location for theoptical network of FIG. 40;

FIG. 42 is a graph that illustrates the positive and negativefrequencies of the delays from FIG. 41;

FIG. 43 illustrates a non-limiting example digital implementation fortranslation to baseband; and

FIG. 44 a vibration correction network for transmission measurements.

DETAILED DESCRIPTION

In the following description, for purposes of explanation andnon-limitation, specific details are set forth, such as particularnodes, functional entities, techniques, protocols, standards, etc. inorder to provide an understanding of the described technology. It willbe apparent to one skilled in the art that other embodiments may bepracticed apart from the specific details disclosed below. In otherinstances, detailed descriptions of well-known methods, devices,techniques, etc. are omitted so as not to obscure the description withunnecessary detail. Individual function blocks are shown in the figures.Those skilled in the art will appreciate that the functions of thoseblocks may be implemented using individual hardware circuits, usingsoftware programs and data in conjunction with a suitably programmedmicroprocessor or general purpose computer, using applications specificintegrated circuitry (ASIC), field programmable gate arrays, one or moredigital signal processors (DSPs), etc.

FIG. 1 shows a first, non-limiting, example embodiment implemented in anOFDR 10. The invention is not limited to an OFDR, but may be applied inany fashion, implementation, or environment to compensate for timevarying phase changes in interference measurements. The OFDR includes aprocessor 12 for controlling a tunable laser 14 and a data acquisitionunit 16. The processor 12 sweeps the tunable laser continuously over thewavelength range of interest with a limited number of mode-hops. Thelight from the tunable laser 14 is directed into an optical networkassociated with the OFDR 10. An input optical coupler 28 splits thelaser light into two paths P1 and P2. The top path P1 is directed to areference interferometer 20.

The reference interferometer 20 is shown as a Mach-Zehnderinterferometer, but could be any form of interferometer, such as aFabry-Perot or Michelson interferometer. The reference interferometershould have two stable arms with minimal dispersion. Optical fiber workswell in this application. The reference interferometer 20 includes anoptical coupler 22 for splitting the light between two paths P3 and P4.P4 is the shorter path and is coupled to an optical coupler 26. Thelonger path P3 delays the light before it reaches the same opticalcoupler 26. The combined light is then provided to a detector 46 whichdetects the intensity of the light and provides it to the dataacquisition unit 16 for processing. The delay difference between the twopaths P3 and P4 of the reference interferometer 20 should be long enoughthat the fine-structure of the laser tuning speed variation is captured.Since most of the tuning speed structure in a laser is due toacousto-mechanical effects below 10 kHz in frequency, the length of thereference interferometer should be chosen such that in normal operationof the OFDR, the frequency of the interference fringes or patternsproduced by the reference interferometer is substantially greater than10 kHz. One example frequency is 40 kHz. The reference interferometerlight from the detector 46 is digitized by the data acquisition unit 16and then used to resample the interferometeric data from near and farinterferometers 30 and 33 (described below) using as one example thetechnique described in U.S. Pat. No. 5,798,521, the contents of whichare incorporated herein by reference. This resampling operation takesdata sampled in equal increments of time, and changes it to data that isin equal increments of wavelength. In other words, the sampled near andfar interferometric measurement data is now linear in wavelength.

The light in path P2 is split again in coupler 28 and directed to nearand far interferometers 30 and 33, respectively. The near interferometer30 includes an optical coupler 31 that splits the input light into twopaths including a shorter path P5, which is coupled directly to anoutput optical coupler 32, and a longer path P6, which is coupled to aninput/output coupler 36. The far interferometer 33 includes a longerpath, (that extra length is shown as an example 5 km fiber loop 35),that delays when the light reaches optical coupler 34. Coupler 34 splitsthat delayed light into a shorter path P7 and a longer path P8. Theshorter path P7 is coupled directly to the coupler 37, and the longerpath P8 is coupled to the input/output coupler 36. The input/outputcoupler 36 combines the light from the longer path P6 in the nearinterferometer 30, and the longer path P8 in the far interferometer 33.The coupler 36 output connects to a connector 38 to which a device undertest (DUT) 40 is coupled by a fiber as shown.

Reflected light from the (DUT) 40 is coupled by the input/output coupler36 and is distributed to the two longer paths P6 and P8 where it iscombined in (interferes with) respective couplers 32 and 37 with lightfrom their respective reference paths P5 and P7. The interference outputfrom coupler 32 is provided to a polarization beam splitter (PBS) 44which provides two orthogonal polarized components of the light S1 andP1 to separate S and P light intensity detectors 48 and 50. The outputfrom the far interferometer 33 is similarly provided to its ownpolarization beam splitter 42, and the intensity of the orthogonal lightpolarizations S2 and P2 are provided to respective detectors 52 and 54.The data acquisition unit 16 digitizes the detected light at eachdetector and provides the digital information (interferometric patternmeasurement data) for processing.

The 5 km of fiber 35 in the far interferometer 33 gives a delay of about25 microseconds. As a result, the measurements made by the farinterferometer 33 occur 25 microseconds after the measurements made bythe near interferometer 30. The two time-offset groups ofinterferometric measurement data provide a quantitative measurement ofthe time-varying nature of the DUT 40. If the frequency of the timevariations affecting the DUT is much smaller than the frequency of thetime delay for the far interferometer 33, (e.g., 25 microsecondscorresponds to 40 kHz, and typical vibration frequencies are below 1kHz), then the phase difference between the two measurements will beproportional to the derivative of the phase difference as a function oftime. The actual phase variation can then be obtained by integrating thephase difference between the two measurements.

FIG. 2( a) illustrates near and far interferometric patterns or“interferograms.” Distortion of the phase appears as compressed andextended periods of the sine wave. This can be seen easily by comparingthe zero crossings for both waveforms. When the interferograms aretransformed into the frequency domain using a Fourier transform, errorsdue to the time-varying changes cause the expected sharp frequency peaksto spread out and to be misshapen as shown in FIG. 2( b).

Applying an inverse Fourier transform to the points in the waveformsegment associated with each widened frequency peak shown in FIG. 2( b)into the time domain provides a measure of the phase of each signal. Anillustration of the phases of both interferometer signals is shown inFIG. 3( a), where one of the signal phases is shown as a dotted line.One signal is delayed with respect to the other. If the phase featuresare fixed characteristics of the DUT, then they will should occur at thesame wavelength for each OFDR laser sweep, and therefore, no such delayshould be present. So the time varying part of the phase signalcorresponds to any delay. Consequently, when the phases of each signalare subtracted, as shown in FIG. 3( b), the static parts of the DUT'sphase variation cancel, and only the dynamic, time varying phasecomponent remains. The remaining phase difference can then beintegrated, (taking into account the proportion as shown in equation (5)below), introduced by the sampling interval, as shown in FIG. 3( c), andthe original time-variant phase reconstructed. This integration may bedone using a numeric integral, of which there are a number of methods,any one of which could be employed here. The reconstructed phase canthen be subtracted from the phase of the original “near” interferometricpattern data to produce a phase measurement free of the effects ofvibration (or any other time varying influences) in the interferometer.

What was just explained graphically and textually is now demonstratedmathematically beginning with an equation for the phase of signal:

φ(t)=θ(ω(t))+β(t)  (1)

where, φ, is the phase of the measured signal, θ is the phase of thesignal that is dependent upon the frequency, ω, of the incident light,and β is the time-variant phase of the path leading to the DUT. Thefrequency, ω, and the time-variant phase, β, are both shown as functionof time, t. In a standard OFDR system, only one measurement of φ as afunction of time is available, and so the frequency and time dependentcomponents of phase, θ and β, cannot be separated. Introducing aslightly delayed version of the laser sweep, produces a second phasemeasurement, where Δ is the delay:

φ′(t)=θ(ω(t−Δ))+β(t)  (2)

This second measurement can then be numerically delayed so that thelaser frequencies of the two functions φ, φ′ are identical. This is aaccomplished by a numerical shift in the data that is equivalent to thedelay Δ introduced by the fiber delay line.

φ′(t+Δ)=θ(ω(t))+β(t+Δ)  (3)

Subtracting the two phase measurements results in:

φ′(t+Δ)−φ(t)=β(t+Δ)−β(t).  (4)

Division by the delay, Δ, gives an expression:

$\begin{matrix}{\frac{{\varphi^{\prime}( {t + \Delta} )} - {\varphi (t)}}{\Delta} = {\frac{{\beta ( {t + \Delta} )} - {\beta (t)}}{\Delta} \approx {\frac{\beta}{t}.}}} & (5)\end{matrix}$

Obtaining useful results often requires a more precise calculation ofthe phase error from the difference in the two signals, which can bedone using Fourier transforms. Starting with the expression in equation(4) of the measured signal,

θ(t)=β(t+Δ)−β(t)  (6)

where θ(t) is the signal that can actually be measured, and β(t) is thesignal to be determined. Fourier transforming the equation results in:

$\begin{matrix}{{\int_{- \infty}^{\infty}{{\vartheta (t)}^{{\omega}\; t}\ {t}}} = {{\int_{- \infty}^{\infty}{{\beta ( {t + \Delta} )}^{{\omega}\; t}\ {t}}} - {\int_{- \infty}^{\infty}{{\beta (t)}^{{\omega}\; t}\ {t}}}}} & (7)\end{matrix}$

doing a change of variables results in:

$\begin{matrix}{{\int_{- \infty}^{\infty}{{\vartheta (t)}^{{\omega}\; t}\ {t}}} = {{\int_{- \infty}^{\infty}{{\beta (t)}^{{\omega}{({t - \Delta})}}\ {t}}} - {\int_{- \infty}^{\infty}{{\beta (t)}^{{\omega}\; t}\ {t}}}}} & (8)\end{matrix}$

and pulling Δ out of the integral over t results in:

$\begin{matrix}\begin{matrix}{{\int_{- \infty}^{\infty}{{\vartheta (t)}^{{\omega}\; t}\ {t}}} = {{^{- {\omega\Delta}}{\int_{- \infty}^{\infty}{{\beta (t)}^{\omega t}\ {t}}}} - {\int_{- \infty}^{\infty}{{\beta (t)}^{{\omega}\; t}\ {t}}}}} \\{= {( {^{{- {\omega}}\; \Delta} - 1} ){\int_{- \infty}^{\infty}{{\beta (t)}^{{\omega}\; t}\ {t}}}}}\end{matrix} & (9)\end{matrix}$

For Δ=0, i.e. no time delay, there is no signal available, and thetime-varying phase cannot be measured. If Δω is very small, the measureof the time-varying phase is poor. Accordingly, slowly varying phaseswill not be well accounted for. Fortunately, as explained above, slowlyvarying effects do not disturb the measurements significantly, andgenerally can be ignored. As Δω approaches 2π, the signal goes to zerobecause the delay is now equal to the period of the signal. For a 25microsecond delay, this effect occurs at 40 kHz. But such highfrequencies are uncommon in optical fiber lengths. Dividing through bythe term in front of the β integral and inverting the transform to findβ results in:

$\begin{matrix}{{\frac{1}{2\pi}{\int_{- \infty}^{\infty}{\lbrack {\frac{\int_{- \infty}^{\infty}{{\vartheta (t)}^{{\omega}\; t}\ {t}}}{( {^{{- {\omega}}\; \Delta} - 1} )}^{- {\omega\tau}}}\  \rbrack {\omega}}}} = {\beta (\tau)}} & (10)\end{matrix}$

From the math above, the following process can be extracted. Measure theinterference pattern data for both the delayed (far) signal and theun-delayed (near) signal. This signal is acquired as a function of laserwavelength, and is therefore considered to be in the frequency domain.Next, both signals are transformed into a time domain, and the timesegment that contains the DUT segment of interest is selected. Thesegment of DUT data is then converted back into the frequency domain.From the segment of DUT data, the phases of the far and the near signalare determined, and the phase difference between those phases iscalculated. The phase difference is Fourier transformed into thefrequency domain and divided by the expression in the denominator ofequation (10). The inverse transform is performed on the result toobtain the time-varying phase component β(t).

Although the above procedures may be implemented using the exampleconfiguration shown in FIG. 1, an alternate, second, example,non-limiting embodiment using a different coupler arrangement as shownin FIG. 4 may be employed. (Like reference numerals refer to likeelements throughout the drawings.) The configuration of the nearinterferometer 30′ and the far interferometer 35′ is somewhat different.Light from coupler 28 is provided to optical coupler 31, and the lightoutput from coupler 31 is split between a polarization controller (PC)60, which aligns the light to be evenly split between the polarizationmodes of the Polarization Beam Splitter (PBS) 44 (e.g., s and ppolarizations), and which provides polarized light to the opticalcoupler 32 and another path that couples directly to the a 1×2input/output coupler 36′. Light reflected from the DUT 40 returnsthrough coupler 36 to coupler 31. A portion of the reflected DUT lightis directed to coupler 32 where it is summed with the light that passedthrough the polarization controller (PC) 60. The far interferometer 35′includes a similar configuration with an input optical coupler 34, apolarization controller 61, and output optical coupler 37. The secondpath output from the optical coupler 34 is coupled to the input/outputcoupler 36′. This embodiment has an advantage relative to the firstembodiment in that the couplers are less expensive and more readilyavailable 2×2 or 1×2 couplers. The 1×4 input/output coupler 36 used inthe first embodiment is not required. Moreover, the overall lightintensity loss in the two interferometers 30′ and 33′ is somewhat lower.But a drawback is that reflections from the polarization beam splitters44 and 42 and the detectors 46-54 can appear in the measurement data.

FIG. 5 illustrates a third, non-limiting, example embodiment of an OFDRthat includes a near interferometer 30″ and an far interferometer 33″.The near interferometer 30″ receives light in a 2×2 coupler 42, theoutput of which is provided to polarization controller PC 1. The secondoutput of the coupler 31 (on the bottom right of coupler 31) is providedto coupler 44, which then provides light to coupler 36″. Light reflectedfrom the DUT 40, returns through coupler 36. A portion of that lightcontinues to coupler 44, where half of the light is then directed alongthe path on the left, connecting couplers 44 and 31. The light is thensummed at coupler 31. The far interferometer 33″ includes a similarcoupler configuration with 2×2 coupler 46 receiving light and outputtingone path to a polarization controller PC2. The two output paths arecombined in output coupler 46, the output of which is provided to the 1by 2 input/output coupler 36″. An advantage of this embodiment is thatreflections from the polarization beam splitters 44 and 42 and thedetectors 46-54 do not appear in the interference pattern measurementdata. A disadvantage, however, is that strong reflections from the DUT40 will be re-circulated and multiple images will occur. If a strongreflector is present at the DUT, light can pass from the right hand pathconnecting coupler 44 to coupler 31, to the left hand path connectingcoupler 31 to coupler 44, and then back to the DUT where it will bereflected again.

A problem encountered with using relatively long delay fiber loops suchas the 5 km fiber loop 35 shown in FIG. 1 is polarization stability—bothas a function of time and wavelength. However, the polarizationstability problem may be overcome using a Faraday Rotator Mirror (FRM)in conjunction with a fiber-optic coupled circulator to produce a longdelay line with a stable polarization. A Faraday Rotator Mirrorcompensates for variations in the state of polarization of receivedlight but returns the light in a polarization that is orthogonal to thepolarization mode in which it was received. FIG. 6 shows a circulator 64which receives light and circulates it to the long fiber delay line 66.The delayed light is reflected by a Faraday Rotator Mirror 68 in apolarization mode orthogonal to the light that entered the input to thecirculator 64. The light that exits the circulator 64 is then caused bythe Faraday Rotator Mirror to be orthogonal to the light that enteredthe circulator's input port. Since the long fiber 66 does not affect thepolarization state of the light entering the circulator 64, it does notaffect the polarization state of the light exiting the circulator 64.

A polarization controller and a polarization beam splitter (PBS) can beused instead of a circulator. FIG. 7 shows incoming light aligned in the“s” polarization mode by a polarization controller 70 before being splitby the polarization beam splitter 72. All of the s-polarized light goesthrough delay 66 and is reflected by the FRM 68. The PBS 72 forwards thereflected light now in the “p” polarization mode. This configuration isless expensive than the configuration shown in FIG. 6. FIG. 8illustrates an OFDR similar to that shown in FIG. 1 but with theinclusion of the polarization stabilizing elements from FIG. 7, whichcould also be included in FIGS. 3 and/or 4.

As mentioned in the background, vibrations can be a problem forinterference measurements. For example, FIG. 9 shows an OFDR 10 coupledto a fiber DUT 40. A vibration source generates vibration wave frontsand expanding traveling waves that impact and vibrate the DUT fiber 40.From the pattern of the traveling waves incident on the DUT 40, alocation of the vibration source, the distance of the vibration sourcefrom the fiber, and a point on the fiber which is closest to the fibersource can be determined. In a similar way, by matching the incidentpattern expected for a given location on the fiber, the vibrationoriginating from that location can be filtered out from among manydifferent vibration sources using phased array antenna principles.

A non-limiting, example prototype OFDR is shown in FIG. 10. The DUT 80includes a reflector 84 coupled to an acetylene gas cell 82 thatproduces a phase artifact in the static part of the interference data.This phase artifact is due to the absorption line of the gas in the celland was chosen to ensure that the method was indeed removing the dynamicphase effects while retaining the static ones. A small coil 86 coupledthe gas cell 82 was subjected to a disturbance (tapping by fingers)during the laser sweep. The laser was swept at about 40 nm per second,and the 50 m delay used in the reference interferometer 20 was used tolinearize the detected interference pattern data to the correctcorresponding laser wavelength by the data acquisition unit 16. Oneexample way to accomplish that compensation process is described in U.S.Pat. No. 5,798,521. The linearized interference pattern data was thenFourier transformed, and the resulting amplitude v. frequency plot isshown in FIG. 11. Since the near and far interferometers will not haveprecisely the same differential lengths, a “phase alignment” reflector88 was used to allow the phases measured by each of the near and farinterferometers to be aligned so that the interference pattern dataappears as if the two interferometers had precisely the same length.

The effects of the vibration disturbance in the measurement path can beseen in width of the base of the gas cell frequency peak in FIG. 11.FIG. 12 is a closer view of the reflection through the gas cell. Thewide spread around the peak base is caused by the time-varyingdisturbance to the optical fiber. The complex data associated with thefiber segment shown in FIG. 12 can be windowed, inverse Fouriertransformed into the time domain, and the phases calculated to produce aphase vs. time plot for each of the near and far interferometers. Thesmall phase delay between the two signals (thin and thick lines) isshown in FIG. 13. The difference between these phases was determined andprocessed as described in equation (10). Subtracting the calculatedtime-variant phase from the measured phase from one of the near or farinterferometers produces a static or time invariant phase shown as athick black line in FIG. 14. For comparison, the original phasecontaining both the time-varying and time-invariant phase components isshown as a thin line.

Using two separate near and far interferometers with separate referencepaths as shown in the above example embodiments results in a number ofadditional problems. First, the necessary splitting of the light intonear and far interferometer reference paths and the coupling mechanismsrequired to get both probe signals from the near and far interferometersinto and out of the DUT results in significant signal loss. Second, withtwo separate interferometers, the two probe signals from the near andfar interferometers will be at different polarizations. If the DUT ispolarization-dependent, which is likely, the resulting interferometricmeasurement data will be different for different probe lightpolarizations. Third, with separate reference paths for the near and farinterferometers, the relative phases between the interferometer patternor fringe data can change as a result of drift caused by temperatureinduced changes in the relative lengths of the reference paths. Verysmall changes (<1 C) in temperature can cause several wavelengths ofchange in the lengths of optical fibers. To overcome these problems, asingle reference path may be used if a delay is introduced to themeasurement arm of the interferometer. The delayed term now appears asan interference term at the delay distance plus the DUT distance. Asingle reference path architecture significantly simplifies the OFDRoptical network and requires fewer optical components, resulting inlower cost and higher reliability.

FIG. 15 is an example of an OFDR that employs a single interferometerreference path while still providing near and far interferometricmeasurement data. The OFDR in FIG. 15 is substantially simpler and morepower-efficient than an OFDR employing multiple reference paths. Lightfrom the tunable laser source is introduced into the network at the“laser in” port. A small portion of the light (1% to 10%) is tapped offand connected to a laser monitoring (LM) network 90 that includes acoupler 92 for receiving the input laser light from coupler 88, aninterferometer, and an absolute wavelength reference. The absolutereference is typically a gas cell 94 with absorption lines within thetuning range of the laser, but a thermally stable etalon could besubstituted with some loss in accuracy. The length of the laser(wavelength) monitoring network 90 is chosen such that it is long enoughto provide high temporal resolution measurements of the laser frequency,but short enough to provide a non-zero frequency response to the laser'stuning speed errors. If the maximum frequency content of the lasertuning speed error is given by f_(L), and the minimum tuning speed (infrequency) of the laser is given by, v_(min), then the wavelengthmonitor interferometer must be chosen such that,

${\frac{4\; f_{L}}{v_{\min}} < D < \frac{1}{4\; f_{L}}},$

where D is the delay of the interferometer in seconds. Using the speedof light, the group index of the fiber, and the geometry of theinterferometer (Mach-Zehnder, Michelson, or Fabry-Perot), the requiredlength of fiber can be readily calculated.

The light from coupler 92 is split between the gas cell 94, whichprovides an absolute wavelength reference detected by detector 96, andcoupler 98 which couples the light to a polarization stabilizationnetwork including a FRM 102, a 400 meter delay loop 104, and a FRM 106.Ultimately, the reflected light is combined in coupler 98, detected atauxiliary detector 100, and provided for processing as the LM monitoredsignal. This LM signal provides a precise measurement of changes in thewavelength of the laser. The gas cell provides absorption lines thatprovide highly accurate measurements of the absolute laser wavelength.Thus, the LM network 90 provides to the data processor absolutewavelength references and the output laser wavelength as a function oftime so that the light intensity interference pattern data can becorrelated with the actual input wavelength that caused that data.

The laser input light from coupler 88 is also received in a singlereference path near and far interferometer. Coupler 112 splits the lightbetween the single reference path, which includes a polarizationcontroller 116 to align the reference light to the transmittingpolarization state of one of the polarizing ports on a polarizationbeam-splitter (PBS) 132, and the measurement path that includes apolarization controller 114 to align the light to one polarization “s₁”before being received at the s-port of a polarization beam splitter(PBS) 118. As a result of the s-polarization at PC 114, nearly all ofthe input light is output by the PBS 118. The PBS output is divided incoupler 120 between a “short path” (which in the two reference pathembodiments above is associated with the near interferometer) that endsin an FRM 126, and a “long path” (which in two reference pathembodiments above is associated with the far interferometer) that endsin an FRM 124 after being delayed in a 14 km loop 122. The lightreflected from both FRMs 124 and 126 is at an orthogonal polarization“p₁” to the input “s₁” light and is combined in coupler 120.

The coupler 120 output is split between a “time shear” path to detector126 and a return path to the PBS 118. These two time-sheared(time-delayed) optical signals from the short and long paths interfereon the detector 136 and provide a highly accurate measurement of thedifferential delay (the time shear) between the long and the short path.The detector 136 output is provided as an input to mixers 140 and 142.

The PBS 118 routes the combined short and long path output light fromthe coupler 120 to port 1 of an optical circulator 128 which couples allthat light to the DUT via port 2. The light from both the short and longdelays has the identical polarization. So any differences in the phasesof the reflected light must be from time variations in the DUT over thetime interval between the two delays. The light reflected from the DUTis coupled from port 2 of the circulator 128 to port 3 of the circulator128 where it is combined with the light from the single reference pathin combiner 130. The circulator 128 could be replaced with a coupler tosave cost but with some degradation in signal-to-noise ratio.

The polarization controller 116 is present in the single reference pathso that the reference light can be split approximately evenly betweenthe s and p states of the PBS 132 connected to the output of the coupler130. The PBS 132 splits the interfering light so that “s₂” polarizationlight is detected at detector 134 and orthogonal “p₂” polarization lightis detected at detector 132. The s and p detectors 134 and 138 measurethe interference patterns or fringes. The s-polarization detector 134provides the s-mode interference pattern signal to a mixer 140 and thena low-pass filter (LPF) 144 as well as directly to a low pass filter 146without any mixing. The p-polarization detector 138 sends the p-modeinterference pattern signal to a mixer 142 and then a low-pass filter(LPF) 148 as well as directly to a low pass filter 150 without anymixing.

There are two responses for the DUT 40 in the signals arriving adetectors 134 and 138: one DUT response took a short path and anotherDUT response took a longer path and arrived later. If we assume adistributed DUT, such as a series of Bragg gratings, then the DUT willbe distributed along some length or distance. FIG. 16 illustrates thecorresponding frequency distribution of these short and long DUTresponse signals. The more distant an optical path, the higher thefrequency of the response interference fringes. Consequently, nearergratings cause lower frequency interference fringes, and more distantgratings cause substantially higher frequency interference fringes. FIG.16 illustrates the spectral distribution of these short path and longpath signals at detectors 134 and 138.

The long path interference pattern signals are at too high of afrequency to pass through the low-pass filter, and as a result, areremoved, leaving just the part of the detected interference patternsignal resulting from the short path. This is referred to as the “near”signal, and there is a near signal for both the s and p detectors:p-near or p₁ and s-near or s₁. The signals that are connected to themixers 140 and 142 are mixed with the “shear” interference signal fromthe detector 136 to frequency translate or downconvert the long pathinterference pattern signals to baseband, or lower frequencies, whilemoving the short path delay signals out of baseband to higherfrequencies. The time shear signal functions as a local oscillatorsignal and has a frequency close to that of the far signal, which causesfrequency translation of the far signal to baseband. The shearinterference signal will track any tuning speed variations such that thefar signal will be mapped back to baseband with very high precision.When each mixed signal is then low-pass filtered, only the signals fromthe long path, referred to as the “far” signal, remain. The far signalfor both the s and p detectors include s₂ and p₂. The four LPF outputscorresponding to interference pattern data from both the long and shortpaths are provided for processing.

When interrogating Rayleigh Backscatter or Bragg gratings, thispolarization state matching is important since any phase differencesbetween the two long and short path probe signals will be interpreted tobe caused by time-variations—not polarization dependence. Using a singlereference signal means that the two long and short path probe signalsare detected in the same polarization.

FIG. 17 is shows a more complete diagram of a single reference pathexample OFDR embodiment. The circulator 128 has been replaced withcoupler 128 to save cost, and the analog detector outputs have beenconverted into digital format in respective analog-to-digital converters152-162 for processing in digital processing block 166, which could bebut is not limited to a field programmable gate array (FPGA). Detailsregarding digital signal processing block 166 and the processor 156 willnow be described.

Data Processing

As explained in the background, the processing and memory requirementsto process interferometeric pattern data at high laser tuning speedsand/or for long distance DUTs very substantial. To reduce thoserequirements, the data set for processing was reduced. A segment ofinterest for the DUT is identified, and the corresponding data isextracted from the overall interferometeric pattern data. The muchsmaller extracted data set is then processed.

There are six steps diagramed in data processing flow of FIG. 18 thatends in calculating the time varying phase component of the reduced dataset. Of those six, the first four steps describe a data reductionprocess.

1. Forming a laser phase signal from a LM interference signal.

2. Forming near and far path delay phase correction signals from thelaser phase signal.

3. Multiplying (or mixing) the delay location back to baseband using thelaser phase signal.

4. Low-pass filtering and decimating the mixed signal.

5. Calculating the phase of the near path and far path segments.

6. Calculating the time varying phase for the segment and removing it.

The laser phase signal is the local oscillator (LO) signal needed tofrequency translate the DUT segment data down to baseband or lowfrequencies. The forming of the delay specific signal determines thelocation of the DUT signal (e.g. 2.752 km) that will be brought back tobaseband. The multiplication process is the mixing process that bringsthis DUT segment to baseband or low frequencies. The low-pass filteringand decimation determine the width or range (e.g. 20 m) of the DUTsegment to be analyzed. Then the near and far phase calculationsdescribed above are performed on the DUT segment data.

There are a variety of ways to perform this processing. Two non-limitingexample methods are described below. The first is called the “NumericalProcessing Method” and processes the data in steps 1-4 using numericalcalculations in a processor or computer by calculating equations and thelike using software computer instructions. The second example methodperforms many of the processing steps 1-4 in digital signal processingcircuitry as the raw data arrives and is called the “Digital ProcessingMethod.” The Digital Processing Method is implemented in hardwarecircuitry.

Software-Based Numerical Signal Processing

1. Laser Phase Calculation

The signals digitized by the analog-to-digital converters 156-162contain information about optical paths from zero meters out to thetotal range of the system, which could be 10′, 100's, 1000's, or evenmore meters. It would be advantageous to be able to extract the signalassociated with a particular location in the fiber (e.g., 2.752 km) oversome specified range (e.g. 20 m) centered on this location. Thisextraction would greatly reduce the amount of data that must be storedand processed to recover the desired information. The process for doingthis segment windowing or interference pattern data extraction firstmeans that the desired signal must be translated to baseband or lowfrequencies and then low-pass filtered.

Converting to baseband is a process performed in most moderncommunications systems. In FM and AM radio broadcasts, many stationsshare the same space, and particular stations are assigned particularfrequencies. Each frequency is a perfect sine wave that the transmittingstation modifies slightly to encode low frequency audio information onthe sine wave. Individual radios reproduce the perfect sine wave at theparticular frequency assigned to the transmitter of interest, commonlyreferred to as the local oscillator (LO) signal, and mix this sine waveor LO signal with the signal received by an antenna. The antenna signalcontains signals from numerous radio stations, and a weaker,time-shifted version of the signal from the station of interest.Multiplying, or mixing, the antenna signal with the local oscillator(LO) signal and low-pass filtering this signal selects out the oneparticular station's signal, and measures the small deviations of thetransmitted signal from the perfect sine wave. These small deviationsare the signal of interest, which in the radio broadcast context is theaudio signal. Signals besides sinewaves can also be used as the basesignals or local oscillators in communications systems, but theprinciple of multiplying and lowpass filtering to select a particularlow-bandwidth signal can still be used.

In interferometic measurements in this case, a desirable goal is toextract information uniquely encoded by its delay in the interferometricsystem. Usually, information about many delay paths is present in thedetected interferometric signal, and it would be very advantageous to beable to ignore or remove information associated with delays that are notof interest. The difficulty is that the base signal here, analogous tothe sine wave in standard radio systems, is not a sine wave, and isdetermined by the delay and the tuning characteristics of theinterferometer tunable laser. These tuning characteristics arecomplicated, and generally not reproducible from measurement tomeasurement.

The innovative approach here provides a process by which the base signalthat is determined by the delay and the laser tuning characteristics canbe calculated for each laser sweep. That calculated signal is then usedto form a local oscillator (LO) signal that will select or extract thespecific interferometric information associated with a particular, butarbitrary delay in the interferometric system.

In an OFDR application, such as illustrated in FIG. 16, a longerdistance along the distributed DUT means higher frequency. Again, thelaser tuning is not perfect, which means the laser will not produce aperfect sine wave. So the digital signal used to mix the desired DUTsegment location data back to baseband is constructed using theinterference signal coming from the Laser Monitor Interferometer (LMI).

At long distributed DUT distances, and with imperfect lasers, one can nolonger assume that the returning light is approximately at the samewavelength as the reference light. In fact one cannot even assume thatthe tuning rate of the reference light is the same as the tuning rate ofthe light returning from the DUT. As a result the earlier describedmethods of processing the fringe data (see e.g., U.S. Pat. Nos.6,900,897, 6,856,400, 6,566,648, 6,545,760, 6,376,830, 5,798,521) willno longer suffice. Instead, a more accurate method involving a carefulaccounting of all of the time delays in the optical and electricalsystems is required.

FIGS. 19 through 27 highlight optical and electrical signal pathslabeled with associated time delays to be used in the reconstruction ofthe complex time-domain response of the DUT. Assume that the incidentlaser field has some optical phase, φ(t). Each signal p(t) measured isthe result of interference between two optical paths highlighted in FIG.19 through 27, and therefore, the measured quantity is always thedifference between two delayed versions of the original laser phase,φ(t). This is required since the laser phase, φ(t), varies too rapidlyto be directly measured. And so, the signal at the LM detector will looklike,

p(t)=p _(τ) +p _(T)−2√{square root over (p _(τ) p _(T))} cos(φ(t−τ_(LM))−φ(t−T _(LM)))  (12)

The delays τ_(LM) and T_(LM) in equation 12 are associated with thepaths highlighted in FIGS. 19 and 20, respectively. The powers “p” maybe assumed constant or at the very least, slowly varying. With thisknowledge, and the knowledge that the laser sweep is monotonic, we cancalculate φ_(LM) from a measured value of p(t),

φ_(LM)(t)=φ(t−τ _(LM))−φ(t−T _(LM)).  (13)

Taking the Fourier Transform of φ_(LM) gives,

Φ_(LM)(ω)=(e ^(−iωτ) ^(LM) −e ^(−iωT) ^(LM) )Φ(ω)  (14)

and if we want to recover the laser phase,

$\begin{matrix}{\frac{\Phi_{LM}(\omega)}{^{- {\omega\tau}_{LM}} - ^{{- {\omega}}\; T_{LM}}} = {\Phi (\omega)}} & (15)\end{matrix}$

To calculate the laser phase numerically, given these equations, theinterference signal present at the LM detector is transformed into thefrequency domain using a Fourier transform. A segment or portion of thetransformed data that is of interest is then windowed around thefrequency peak at the location corresponding to the delay associatedwith the LM interferometer. The windowing extracts only the dataassociated with the positive frequencies of the laser monitorinterferometer. The windowing is achieved by multiplying the transformeddata by a window function centered at the peak location and wide enoughto encompass the peak (see FIG. 28). Many different window functionscould be used, ranging from a simple square wave type window (as shownin FIG. 29) to a more complicated Blackman window. An inverse transformthen takes this windowed data back to the time domain. The phase of theresulting complex data is then calculated as a function of time using afour quadrant arc tangent to convert the real and imaginary parts ofeach entry in the extracted data array to a phase, and a commonly known“phase unwrap” method that adjust the phase that is limited to a 0 to 2πrange to the larger range needed to represent the total tuning andstored in memory. The laser monitor phase (LM) is actually thedifference between two time-shifted versions of the laser phase asdescribed by equation 13. To calculate the laser phase from theextracted LM, the LM phase is divided by the denominator shown inequation 15. When performing these calculations numerically, however,the LM phase can also be used as will be shown below.

2. Calculating Near and Far Delay Phases

The next data processing step involves calculating the phases specificto the delays associated with the detected un-delayed (short path ornear) and delayed (long path or far) interference pattern signals. Thenear and far phases can be related to the laser phase using similarrelationships as for the LM phase. These relationships are shown below.Assume that the s and p channels have been constructed to be identicalin delays, and we will therefore only treat the s terms, with theunderstanding that the p terms are identical. The paths for theindividual path delays, τ_(rn), τ_(n), τ_(DUT), τ_(rf), τ_(f), τ_(sn),and τ_(sf), are highlighted in FIGS. 21-27.

φ_(snear)(t)=φ(t−τ _(rn))−φ(t−τ _(n)−τ_(DUT))  (16)

φ_(sfar)(t)=φ(t−τ _(rf))−φ(t−τ _(f)−τ_(DUT))−φ(t−τ _(sn))+φ(t−τ_(sf))  (17)

where φ_(snear) is the phase measured for the near path through the DUT,and φ_(sfar) is the phase measured for the far path through the DUT.

Taking the Fourier transform of equations 16 and 17 yields:

Φ_(snear(ω)) =[e ^(−iωτ) ^(rn) −e ^(−i)ω(τ ^(n) ^(+τ) ^(DUT)⁾]Φ(ω)  (18)

and

Φ_(sfar)(ω)=└e ^(−iωτ) ^(rf) −e ^(−i)ω(τ ^(f) ^(+τ) ^(DUT) ⁾ −e ^(−iωτ)^(sn) +e ^(−iωτ) ^(sf) ┘Φ(ω)  (19)

where, ω is the frequency, Φ(ω) is the Fourier Transform of the phase ofthe laser signal, and Φ_(sfar)(ω) is the Fourier Transform of the phaseof the signal present for a delay path specified by τ_(DUT).

Using the relationship between the LM phase and the laser phase shownabove, one can derive equations relating the near and far phases to theLM phase.

$\begin{matrix}{{\Phi_{snear}(\omega)} = {\frac{^{- {\omega\tau}_{m}} - ^{- {{\omega}{({\tau_{n} + \tau_{DUT}})}}}}{^{- {\omega\tau}_{LM}} - ^{{- {\omega}}\; T_{LM}}}{\Phi_{LM}(\omega)}}} & (20) \\{{\Phi_{sfar}(\omega)} = {\frac{^{- {\omega\tau}_{rf}} - ^{- {{\omega}{({\tau_{f} + \tau_{DUT}})}}} - ^{- {\omega\tau}_{sn}} + ^{- {\omega\tau}_{sf}}}{^{- {\omega\tau}_{LM}} - ^{{- {\omega}}\; T_{LM}}}{\Phi_{LM}(\omega)}}} & (21)\end{matrix}$

where, Φ_(LM)(ω) is the Fourier transform of the laser monitor phase,and τ_(LM) and T_(LM) are the delays through the paths highlighted inFIGS. 19 and 20.

The calculated LM phase from the LM interference signals is firsttransformed into the frequency domain using a complex Fourier transform.This transformed phase is then multiplied by the near and far complexcoefficients relating the LM phase to the near and far phases as shownin equations 20 and 21. Because there are poles in these coefficientswhen the denominator goes to zero, (see FIG. 29 at graph (b)), the datais windowed such that it goes to zero at frequencies at and after thefirst pole. For example, a window function formed by a Hanning windowthat has a value of one at D.C. and goes to zero at the first pole andthere after can be used to multiply the data in the transform domain.See FIG. 29.

In doing this processing, both positive and negative frequencies must beincluded and windowed. When an FFT is performed on a real data set, thepositive frequencies appear in the first half of the data and thenegative frequencies appear in the second half of the data, as shown inFIG. 30 at graph (a). To window both halves, a window is used thatwindows both the positive and negative frequencies, as shown in FIG. 29(c). Here the window function for the negative frequencies is the mirrorof the window function for the positive frequencies.

After the near and far data phases have been calculated and windowedappropriately, the two data sets are then transformed back into the timedomain to form the phases specific to the near and far signals.

3. Numerical Mixing to Baseband

Once the near and far phases have been calculated, the original near andfar interferometric data sets can be mixed with the cosine and sine ofthese phases to bring the desired location to baseband. The measurednear and far signals can be expressed as

s _(near)(t)=cos [φ_(near)(t)+θ(ω(t))+β(t)]  (22)

and

s _(far)(t)=cos └φ_(far)(t)+θ(ω(t−Δ))+β(t)┘  (23)

To frequency translate the desired segment of DUT to baseband, themeasured near and far signals are multiplied by the sine and cosine ofthe near and far phases as shown:

$\begin{matrix}\begin{matrix}{{{Re}\{ s_{{near},{mixed}} \}} = {{\cos \lbrack {{\phi_{near}(t)} + {\theta ( {\omega (t)} )} + {\beta (t)}} \rbrack} \cdot {\cos \lbrack {\phi_{near}(t)} \rbrack}}} \\{= {{\frac{1}{2}{\cos \lbrack {{\theta ( {\omega (t)} )} + {\beta (t)}} \rbrack}} +}} \\{{\frac{1}{2}{\cos \lbrack {{2{\phi_{near}(t)}} + {\theta ( {\omega (t)} )} + {\beta (t)}} \rbrack}}}\end{matrix} & (24) \\\begin{matrix}{{{Im}\{ s_{{near},{mixed}} \}} = {{\cos \lbrack {{\phi_{near}(t)} + {\theta ( {\omega (t)} )} + {\beta (t)}} \rbrack} \cdot {\sin \lbrack {\phi_{near}(t)} \rbrack}}} \\{= {{\frac{1}{2}{\sin \lbrack {{\theta ( {\omega (t)} )} + {\beta (t)}} \rbrack}} +}} \\{{\frac{1}{2}{\sin \lbrack {{2{\phi_{near}(t)}} + {\theta ( {\omega (t)} )} + {\beta (t)}} \rbrack}}}\end{matrix} & (25) \\\begin{matrix}{{{Re}\{ s_{{far},{mixed}} \}} = {\cos {\lfloor {{\phi_{far}(t)} + {\theta ( {\omega ( {t - \Delta} )} )} + {\beta (t)}} \rfloor \cdot \cos}\lfloor {\phi_{far}(t)} \rfloor}} \\{= {{\frac{1}{2}{\cos \lbrack {{\theta ( {\omega ( {t - \Delta} )} )} + {\beta (t)}} \rbrack}} +}} \\{{\frac{1}{2}{\cos \lbrack {{2{\phi_{near}(t)}} + {\theta ( {\omega ( {t - \Delta} )} )} + {\beta (t)}} \rbrack}}}\end{matrix} & (26) \\\begin{matrix}{{{Im}\{ s_{{far},{mixed}} \}} = {\cos {\lfloor {{\phi_{far}(t)} + {\theta ( {\omega (t)} )} + {\beta (t)}} \rfloor \cdot \sin}\lfloor {\phi_{far}(t)} \rfloor}} \\{= {{\frac{1}{2}{\sin \lbrack {{\theta ( {\omega ( {t - \Delta} )} )} + {\beta (t)}} \rbrack}} +}} \\{{\frac{1}{2}{\sin \lbrack {{2{\phi_{far}(t)}} + {\theta ( {\omega ( {t - \Delta} )} )} + {\beta (t)}} \rbrack}}}\end{matrix} & (27)\end{matrix}$

4. Low Pass Filtering and Decimating

With the desired segment of DUT signals at baseband, they are lowpass-filtered using a decimating filter. In the equations above, thesecond term in the expression has a frequency of twice the original.When the signal is low-pass filtered, this term is eliminated yielding:

$\begin{matrix}{{{Re}\{ s_{{near},{mixed}} \}} = {\frac{1}{2}{\cos \lbrack {{\theta ( {\omega (t)} )} + {\beta (t)}} \rbrack}}} & (28) \\{{{Im}\{ s_{{near},{mixed}} \}} = {\frac{1}{2}{\sin \lbrack {{\theta ( {\omega (t)} )} + {\beta (t)}} \rbrack}}} & (29) \\{{{Re}\{ s_{{far},{mixed}} \}} = {\frac{1}{2}{\cos \lbrack {{\theta ( {\omega ( {t - \Delta} )} )} + {\beta (t)}} \rbrack}}} & (30) \\{{{Im}\{ s_{{far},{mixed}} \}} = {\frac{1}{2}{\sin \lbrack {{\theta ( {\omega ( {t - \Delta} )} )} + {\beta (t)}} \rbrack}}} & (31)\end{matrix}$

The original near and far interference measurement data was sampled at ahigh sampling rate, or a fine time increment, so that the bandwidth wassufficient for the long delays. Now that the data is in baseband and hasbeen filtered, it can be decimated to, in effect, reducing the samplingrate or increase the time increment. This has the effect of selectingthe desired section of DUT fiber in the data set with a total lengthdetermined by the decimation factor. This process significantly reducesthe data size for storage and further processing. For example, anynumber of known filter functions can be used to low pass filter anddecimate these data sets numerically.

5. Calculating Phase of Near Path and Far Path Segments

The phases of the near and far signals calculated in step 4 above arecalculated using a four quadrant arctangent and the real and imaginaryparts of the near and far signals. These near and far phases nowcorrespond to the phase signals, φ(t) and φ(t), respectively describedin equations 1 and 2 above.

6. Calculating and Removing Time Varying Phase

The two phase signals calculated in step 5 above can then be used asdescribed in equations 3 through 10 above to calculate the time varyingphase of the DUT path. This calculation involves the time shifting ofthe far phase as described in equation 3, the subtraction of the twophases as described in equation 4, and the coversion of this phasedifference into the time-varying component of the phase as described inequations 5 or 10, (equation 10 is a more precise calculation).

Hardware-Based Digital Signal Processing (DSP) Approach

The software based numerical processing described above requires thatthe entire interferometric data set be mathematically transformedseveral times. Because there can be more that ten million points perdata set for long DUTs, this can be a very resource consuming process interms of time, data processing operations, and memory. It can be viewedas a “brute force” approach. An alternative and more efficient approachdescribed below digitally processes signals as they arrive atappropriately configured digital signal processing circuitry. FIG. 30shows a schematic of a non-limiting example of such configured digitalprocessing circuitry which can be implemented, if desired, as a fieldprogrammable gate array (FPGA). The processing steps to be implementedby the digital processing are the same as described above for thesoftware based numerical processing approach, but the processing isaccomplished differently and more efficiently as described below.

In general, the digital signal processing hardware, in this non-limitingexample an FPGA 166, selects or extracts the data associated with adesired segment of a DUT fiber to be analyzed and in this way greatlyreduces the amount of data to be processed. The Laser Monitor (LM)interferometric signal enters the FPGA as a digital number from ananalog-to-digital converter. This sequence of numbers representative ofpower at the LM detector is translated into a series of numbersrepresentative of the phase derivative (frequency) of the signal presentat the LM detector. The center location of the DUT fiber segment isdetermined by interferometric digital data stored in a shift register(there is a shift register for each light intensity detector) which isloaded into a phase translation module. The width of the DUT segment isdetermined by a cut-off frequency of a decimating digital low-passfilter (the cut off frequency can be programmed via the processor). Thisphase derivative is also re-scaled inside a LM-to-freq module to accountfor the length (delay) of the LM interferometer.

Referring to the digital processing block 166 shown in FIG. 30, the fourinput signals include the laser monitor signal (LM signal), the two setsof interference signals for the two detected polarization states, s andp, that took the near path, and the two interference signals for the twodetected polarization states, s and p, that took the far path. The LMsignal is converted to an estimation of the phase derivative of thelaser phase by the LM to frequency module 160, that is described in moredetail below and in FIG. 36. The phase derivative signal enters a phasetranslation module 162 that calculates the expected phase values fordelays matching the near and far phase terms, also described below andin FIG. 37. The calculated near phase is used to address a pair oflook-up tables for the cosine 166 and the sine 168. The calculated farphase is used to address a pair of look-up tables for the cosine 170 andthe sine 172.

The output of the near cosine look-up table is then multiplied by thenear s polarization signal delayed through the data delay register 174to compensate for the latency in the LM to frequency module 160. Themultiplication is carried out by a hardware multiplier 176, the outputof which feeds a decimating, digital, low-pass filter (LPF) 178. Theoutput of this filter is the real value of the near s polarizationsignal at the DUT delay of interest. The output of the near sine look-uptable is then multiplied by the near s polarization signal delayedthrough the data delay register 174 to compensate for the latency in theLM to frequency module 160. The multiplication is carried out by ahardware multiplier 180, the output of which feeds the decimating,digital, low-pass filter (LPF) 182. The output of this filter is theimaginary value of the near s signal at the delay of interest.

The output of the near cosine look-up table is then multiplied by thenear p polarization signal delayed through the data delay register 184to compensate for the latency in the LM to frequency module 160. Themultiplication is carried out by a hardware multiplier 186, the outputof which feeds the decimating, digital, low-pass filter (LPF) 188. Theoutput of this filter is the real value of the near s polarizationsignal at the delay of interest. The output of the near sine look-uptable is then multiplied by the near p polarization signal delayedthrough the data delay register 184 to compensate for latency in the LMto frequency module 160. The multiplication is carried out by a hardwaremultiplier 190, the output of which feeds the decimating, digital,low-pass filter (LPF) 192. The output of this filter is the imaginaryvalue of the near s polarization signal at the DUT delay of interest.

The output of the far cosine look-up table is multiplied by the far spolarization signal that has been delayed through the data delayregister 194 to compensate for the latency in the LM to frequency module160. The multiplication is carried out by a hardware multiplier 196, theoutput of which feeds the decimating, digital, low-pass filter (LPF)198. The output of this filter is the real value of the far spolarization signal at the DUT delay of interest. The output of the farsine look-up table is then multiplied by the far s polarization signaldelayed through the data delay register 194 to compensate for thelatency in the LM to frequency module 160. The multiplication is carriedout by a hardware multiplier 200, the output of which feeds thedecimating, digital, low-pass filter (LPF) 202. The output of thisfilter is the imaginary value of the far s polarization signal at thedelay of interest.

The output of the far cosine look-up table is then multiplied by the farp polarization signal delayed through the data delay register 204 tocompensate for the latency in the LM to frequency module 160. Themultiplication is carried out by a hardware multiplier 206, the outputof which feeds the decimating digital low-pass filter (LPF) 208. Theoutput of this filter is the real value of the far s polarization signalat the DUT delay of interest. The output of the far sine look-up tableis then multiplied by the far p polarization signal delayed through thedata delay register 204 to compensate for the latency in the LM tofrequency module 160. The multiplication is carried out by a hardwaremultiplier 210, the output of which feeds the decimating digitallow-pass filter (LPF) 212. The output of this filter is the imaginaryvalue of the near s signal at the DUT delay of interest.

1. DSP Laser Monitor Processing

Digital signal processing can be used to advantage to convert the lasermonitor (LM) interference signal to a phase signal as the signal arrivesat the FPGA 166 without having to Fourier Transform the data. Thissimpler conversion can be achieved with just a small level of latency inthe FPGA logic.

FIG. 31 illustrates the signal arriving from the LM interferometerdetector 100. Each rising edge of the LM interferometer detector sinewave signal, which is here illustrated to be the first positive pointfollowing a negative point, represents one cycle, or 2π radians. Giventhe discrete values and binary data representations within the digitalcircuits, a power of 2 is used to represent one full cycle, as istypically done in digital synthesis. FIG. 32 shows the derivative of thephase as calculated from the signal in FIG. 31. One cycle, as defined bythis rising edge definition (above), is 15 clock or sample periods.Choosing an 11-bit representation of the phase, then the averageincrement in phase for the 15 samples is:

$\begin{matrix}{{\Delta\phi}_{ave} = {\frac{2^{n} - 1}{N} = {\frac{2^{11} - 1}{15} = {136.5333333\mspace{14mu} \ldots}}}} & (31)\end{matrix}$

But these are integer computations, so the fractional part cannot behandled directly. Instead, the remainder 8 of the division (2¹¹−1)/15 isdistributed among the 15 samples in the period of the fringe leaving 7entries of 136, 8 entries of 137, and average value of 136.5333 . . . .Since division is a costly digital operation in time and resource, alook-up table is constructed matching the number of samples in a cyclewith the base value (e.g. 136) and the number of incremented value (e.g.8 entries of 136+1). For a given interferometer length, sample speed,tuning rate and tuning variation, the number of possible samples percycles can be calculated, and is typically in the hundreds, and so thetable is of manageable size.

FIGS. 33 and 34 show a digital schematic of one possible way toimplement this algorithm in digital hardware. FIG. 33 converts eachrising edge of the digitized waveform into a single digital high levelfor one clock cycle using a delay latch 220 to store the LM sample ateach clock. The delayed sample is compared to zero in the digitalcomparator 222, and if the value is greater than 0, the comparator 222produces a one, and otherwise a zero. The current sample is compared tozero in the digital comparator 224, and if the value is less than 0,comparator 224 produces a one, and otherwise a zero. The comparatoroutputs are ANDed in gate 226 to produce a signal representing a LaserMonitor Rising Edge (LMRE) signal. This conversion of the analoginterference signal into a series of zero-crossing digital pulses couldalso be achieved with an analog comparator prior to the digitalcircuitry.

FIG. 34 shows the processing of this digital pulse train of zerocrossings. At each pulse, a counter 230 is reinitialized to one and thenbegins counting the number of clock cycles until the next pulse arrives.When the next pulse arrives, the count value addresses a position in anN-position long, p-bit wide shift register 232. One non-limiting of N isaround 256. The counter value is also the data value written into theshift register 232. The length of the shift register, N, must be atleast as long as the longest period of the laser monitor LMinterferometer.

The rising edge pulse sequence also goes into an N-position shiftregister 228. When a pulse shifts out of the N-position shift register228, the number on the output of the p-bit wide shift register is usedto address a look-up table 234 that contains the quotient and remainderof the division of the digital number representing one period in phaseand the number of clock-cycles in the period (the address). Theremainder is loaded into a down counter 238, and as long as the downcounter 238 is greater than zero, one is added to the quotient in summer240. When the value of the down counter drops below zero, zero is addedto the quotient number in summer 240. This fills a shift register 242with the derivative of the LM phase.

The derivative of the LM phase is stored in the register 242 as an“array.” Recall that the desired signal is the phase of the laser field.We can increase the accuracy of the laser phase signal produced by thecircuit shown in FIG. 34 by processing it with a digital filter that hasa complex spectrum correcting for the effects of the measurementapproach. Also, recall that the relationship between the LM phase andthe laser phase is given by:

$\begin{matrix}{\frac{\Phi_{LM}(\omega)}{^{{- {\omega}}\; \tau_{LM}} - ^{{- {\omega}}\; T_{LM}}} = {\Phi (\omega)}} & (32)\end{matrix}$

This is a nice analytic result, but there is a pole at zero. As aresult, φ grows too rapidly. If, instead, we calculate the derivative ofthe laser phase, we get,

$\begin{matrix}{\frac{{\omega\Phi}_{LM}(\omega)}{^{{- {\omega}}\; \tau_{LM}} - ^{{- {\omega}}\; T_{LM}}} = {{{\omega\Phi}(\omega)}.}} & (33)\end{matrix}$

Here, there is a zero canceling the pole at zero, and the expression canbe calculated. If τ_(LM) is zero, then the Taylor expansion of thetransfer function may be calculated as follows:

$\begin{matrix}{{( {\frac{1}{T_{LM}} - \frac{\omega}{2} - \frac{T_{LM}\omega^{2}}{12} - \frac{T_{LM}^{3}\omega^{4}}{720} - \frac{T_{LM}^{5}\omega^{6}}{30240}} ){\Phi_{LM}(\omega)}} = {{\omega\Phi}(\omega)}} & (34)\end{matrix}$

Using this expression, a Finite Impulse Response (FIR) filter issynthesized that converts the measured phase at the Laser Monitordetector into the derivative of the laser phase. The derivative of thelaser phase is calculatedin the time domain using:

$\begin{matrix}{{{\frac{1}{T_{LM}}{\phi_{LM}(t)}} - {\frac{1}{2}\frac{}{t}{\phi_{LM}(t)}} + {\frac{T_{LM}}{12}\frac{^{2}}{t^{2}}{\phi_{LM}(t)}} - {\frac{T_{LM}^{3}}{720}\frac{^{4}}{t^{4}}{\phi_{LM}(t)}} - {\frac{T_{LM}^{5}}{30240}\frac{^{6}}{t^{6}}{\phi_{LM}(t)}}} = {\frac{}{t}{\phi (t)}}} & (35)\end{matrix}$

Then the derivatives of φ_(snear) and φ_(sfar) are calculated simply bysumming shifted versions of this phase. Of course, the Taylor expansionis one non-limiting example method of calculating the time-domainfilter.

Another method of designing the filter is to calculate the complexspectrum of the coefficients relating the LM phase to the laser phaseshown above in equation 33. The expression is windowed to eliminate thepoles as illustrated in the example in FIG. 35. The Figure plots theamplitude of the laser phase correction function in the frequency domainfor a 1600 ns delay Laser Monitor Interferometer. There is a pole around600 kHz, and the windowing is used to suppress the “explosion” of thefunction at that frequency. The expression is then Fourier transformedback into the time domain in order to obtain the coefficients of the FIRfilter, as illustrated in FIG. 36. The Figure plots the impulse responseobtained from the Fourier transform of the windowed phase correctionfunction. These values are the coefficients on the FIR filter used tocorrect the signal from the Laser Monitor Interferometer to form thelaser phase signal. When the data is windowed to eliminate the poles,the bandwidth of the transfer function is reduced—sometimesdramatically—greatly reducing the noise affecting the signal.

The phase signal calculated in this way will have a latency (delay frominput to output in clock cycles) equal to the longest possible period ofa cycle, which will occur at the slowest tuning rate of the laser, andthe length of the FIR filter. All of the incoming signals will need tobe delayed to match this latency.

2. DSP-Based Calculation of Near and Far Delay Phases

As in the numerical processing section above, the s and p channels havebeen constructed to be identical in delays are assumed, and we willtherefore only treat the s terms, with the understanding that the pterms will be identical. The near and far phases are again described by:

φ_(snear)(t)=φ(t−τ _(rn))−φ(t−τ _(n)−τ_(DUT))  (36)

and,

φ_(sfar)(t)=φ(t−τ _(rf))−φ(t−τ _(f)−τ_(DUT))−φ(t−τ _(sn))+φ(t−τ_(sf)).  (37)

With the laser phase signal constructed. it is a simple process toconstruct the phases of the near and far delay terms. This constructionmay be achieved by implementing a box-car, or two-tap filter where thelength of the filter, or, equivalently, the separation of the two tapsis equal to the delay of the DUT location desired. FIG. 37 shows animplementation of this technique using a long, (e.g., 17,000 element),shift register with 6 taps. The optical and electronic design can bemade so that the three front taps are set at zero, resulting in onlythree taps. The more general case, however is shown, along with theaccumulators (the summers) that integrate the data so that the nearphase and the far phase are obtained.

3. DSP-Based Mixing the Signal to Baseband

The mixing process is the same as described above in the numericalprocessing section. However, in this case, the sine and cosinecalculations are replaced with sine and cosine look-up tables 166-172shown in FIG. 30, and the multiplies perform using hardware multipliers176-210 as shown in FIG. 30.

4. DSP-Based Low Pass Filtering and Decimation

The low pass filtering may be implemented with an FIR decimating filter.Decimating filters reduce the signal bandwidth and also lower thesampling rate. The reduced bandwidth no longer requires a high samplerate, and it is advantageous to operate on fewer samples if there is noloss in signal fidelity. Although this particular implementation of adecimating filter is described, any suitable filter may be used ordesigned.

To obtain a sharp frequency filter cut-off, a Blackman Windowed Syncfunction is calculated for a decimation factor of 64, as shown in FIG.38. The Figure shows a six-segmented Blackman Windowed Sync function.The digital value for each of these segments of the filter is loadedinto the circular shift registers shown in FIG. 39. One non-limitingexample implementation of this 6-segment digital filter with adecimation factor of 8 is shown in FIG. 39. The top shift registercontains the digital product of the generated delay signal and theacquired signal. On each clock cycle, the digital number in each blockadvances one register position to the right. The smaller shift registersbelow contain the values of the segments shown in FIG. 38. The top shiftregister accepts the data coming out of the mixer. The multipliersmultiply the incoming data by the coefficients held in the smallercircular shift registers, not shown here is the logic that triggers theoutput of a decimated sample every 8 clock cycles, and also clears allof the accumulators (sets to zero) so that the next sample can becalculated. On each clock cycle, each digital number moves one block tothe right also, but because this is a circular register, the value onthe far left is re-circulated to the first block. Also, on each clockcycle, the data in the blocks connected to the multiplier via arrows ismultiplied together and added to the accumulator shown. After eightclock cycles, the value in all of the accumulators is summed to producea single output sample. The accumulators are also cleared on this eightclock so that they can begin accumulation of the next sample on the nextclock cycle.

The process steps 5 and 6 are performed as described above for thesoftware-based numerical processing example embodiment.

Other Example Embodiments

If bandwidth is a limiting factor, the optical network can be modifiedas shown in FIG. 40. In this embodiment, an additional delay line 262has been added to the reference path. The length of this delay line ischosen such that the “near” reflections are mapped to negativefrequencies, and the “far” terms remain mapped to positive frequencies.FIG. 41 shows the apparent location of the reflection features if oneassumes a short (effectively zero) length reference path. Also shown isthe overall bandwidth of the signal at 100 MHz for a 4 nm/sec tuningrate, and the apparent location of a 6 km reference delay. If we place a6 km delay in the reference, then all frequencies are measured from thisdelay, and we end up with a signal spectrum like the one shown in FIG.42, which is now noted to have a bandwidth of 66 MHz instead of 100 MHz.

It is also possible to implement the vibration tolerance techniquewithout the use of an analog multiplier or mixer if the samplingfrequency is sufficiently high. In that case, an optical network likethe example shown in FIG. 44 may be advantageous because of thereduction in bandwidth required. In this example, a 120 Ms/s converterwould be used to convert the combined near and far signals, and ahardware multiplier would be used to perform the mixing in a digitalformat. The signals could then be processed in an FPGA 166 similar tothat described above, or just in the processor 156.

Example Applications

This measurement technique can be applied to many applications. Forexample, it can be applied to OFDR measurements of Rayleigh backscatterin optical fiber. Information about the local scatter intensity, phase,and time-variance of the phase will be available for each section alonga DUT fiber including very long DUT fibers. This spatial resolution ofthe time-variant measurement is determined by the sweep-rate and thehighest frequency of the acoustic signal present. Having the ability toaccurately measure the spectrum of the Rayleigh scatter from an opticalfiber has great utility, e.g., distributed temperature or strain sensingin high vibration or noisy environments (e.g., aircraft, power plants,ships, etc.). Further, immunity to time-varying effects of the fiberallows the laser scan rate to be slowed, increasing the operationaldistance range of the system. As a result, the acoustic immunity can beextended in the range of thousands of meters. This additional distancerange is another important improvement in the utility of the instrument.

The use of Rayleigh scatter for the sensing means that every section offiber is reflecting light at every point in the scan. Acoustic signalscan then be measured throughout the duration of the scan. If the laseris scanned up and then down in a continuous triangle-wave fashion, thennearly continuous monitoring of the acoustic signals incident on thefiber can be achieved. Each one-meter section of fiber over aone-thousand meter length of optical fiber can then be used as anindependent microphone. The distributed nature of the fiber acousticsensing permits the fiber to be used as a phased acoustic array. In thisway, acoustic signal processing can be used to locate and identifyacoustic sources. Further, ambient sound can be used to form images ofthe surrounding physical features. Implementing a distributed acousticsensor in a marine environment has great utility in the tracking ofvessels and large animals (such as whales).

As another application, in many chemical processing facilities,temperature is a critical parameter. Knowledge of the temperature over alarge volume has significant value. Due to turbulence in the fluids,these environments tend to be acoustically noisy. Here, then, immunityto vibration represents a significant improvement in utility.

In terrestrial applications, this complex acoustic sensing enabled by aphased array can be used for intrusion sensing in a room or around aperimeter. It can also be used to extract single sources among acacophony of different sources that are spatially separated, such as anindividual speaking in a crowded room. A further application would be aninexpensive, distributed seismograph.

If high resolution Rayleigh scatter measurements can be obtained overlong distances (>100 meters) then scatter correlation, as described inprovisional filing “Correlation and Keying of Rayleigh ScatterMeasurements for Loss and Temperature Measurements” could be used as asecurity tool for identifying tampering in a fiber network (such as theaddition of a small tap).

Although various embodiments have been shown and described in detail,the claims are not limited to any particular embodiment or example. Noneof the above description should be read as implying that any particularelement, step, range, or function is essential such that it must beincluded in the claims scope. The scope of patented subject matter isdefined only by the claims. The extent of legal protection is defined bythe words recited in the allowed claims and their equivalents. No claimis intended to invoke paragraph 6 of 35 USC §112 unless the words “meansfor” are used.

1. A method for processing interference pattern data generated by aninterferometer, where the interferometer provides a laser signal from atunable laser along a given optical path having an associated path delayand to a reference optical path and combines light reflected from thegiven optical path and from the reference path thereby generating theinterference pattern data, comprising: estimating a first laser opticalphase of the laser signal; calculating an expected complex response forthe given optical path based on the estimated laser optical phase;multiplying the interference pattern data from the interferometer by theexpected complex response to generate a product; and filtering theproduct to extract interference pattern data associated with the givenoptical path from the interference pattern data generated by theinterferometer.
 2. The method in claim 1, wherein the given optical pathis associated with a device under test (DUT).
 3. The method in claim 1,wherein the step of calculating an expected complex response for thegiven optical path based on the estimated laser optical phase furthercomprises: estimating a delayed version of the laser optical phase ofthe laser signal; determining a difference phase between the delayedversion of the estimated laser optical phase and the estimated firstlaser optical phase; and calculating the cosine of the difference phaseto form the real part of the expected complex response; and calculatingthe sine of the difference phase to form the imaginary part of theexpected complex response.
 4. The method in claim 3, further comprising:low pass filtering and decimating the real and imaginary parts of theexpected complex response to extract interference pattern dataassociated with the given optical path from the interference patterndata generated by the interferometer.
 5. The method in claim 1, whereinestimating the laser optical phase includes: coupling a portion of thelaser light to a second interferometer; converting an interferencefringe signal from the second interferometer into a digital signalcorresponding to the interference pattern data, the digital signal beinga sampled form of the interference fringe signal; estimating the laserphase based upon the digital signal.
 6. The method in claim 5, furthercomprising: estimating a first derivative of the laser optical phasebased in the digital signal including: Fourier transforming the digitalsignal; windowing the transformed signal to identify a portion of thetransformed signal that corresponds to the given optical path delay;inverse Fourier transforming the windowed signal; and computing thephase of the signal.
 7. The method in claim 5, further comprising:estimating a second derivative of the laser optical phase based upon thedigital signals by identifying zero crossings of the digital signal, andcounting a number of samples between the zero crossings of the digitalsignal.
 8. The method in claim 7, wherein the step of calculating anexpected complex response for the given optical path based on theestimated laser optical phase further comprises: estimating a delayedversion of the second derivative of the laser optical phase; calculatinga running sum of the second derivative of the laser optical phase, wherea length of the running sum is associated with a length of the givenoptical path delay; accumulating the running sum; calculating a sine ofthe accumulated sum to form the imaginary part of the expected complexresponse; and calculating a cosine of the accumulated sum to form thereal part of the expected complex response.
 9. The method in claim 8,further comprising: low pass filtering and decimating the real andimaginary parts of the expected complex response to extract interferencepattern data associated with the given optical path from theinterference pattern data generated by the interferometer.
 10. Apparatusfor processing interference pattern data generated by an interferometer,where the interferometer provides a laser signal from a tunable laseralong a given optical path having an associated path delay and to areference optical path and combines light reflected from the givenoptical path and from the reference path thereby generating theinterference pattern data, comprising: means for estimating a firstlaser optical phase of the laser signal; means for calculating anexpected complex response for the given optical path based on theestimated laser optical phase; means for multiplying the interferencepattern data from the interferometer by the expected complex response togenerate a product; and means for filtering the product to extractinterference pattern data associated with the given optical path fromthe interference pattern data generated by the interferometer.
 11. Theapparatus in claim 10, wherein the given optical path is associated witha device under test (DUT).
 12. The apparatus in claim 10, wherein themeans for calculating an expected complex response for the given opticalpath based on the estimated laser optical phase further comprises: meansfor estimating a delayed version of the laser optical phase of the lasersignal; means for determining a difference phase between the delayedversion of the estimated laser optical phase and the estimated firstlaser optical phase; and means for calculating the cosine of thedifference phase to form the real part of the expected complex response;and means for calculating the sine of the difference phase to form theimaginary part of the expected complex response.
 13. The apparatus inclaim 12, further comprising: means for low pass filtering anddecimating the real and imaginary parts of the expected complex responseto extract interference pattern data associated with the given opticalpath from the interference pattern data generated by the interferometer.14. The apparatus in claim 10, wherein means for estimating the laseroptical phase includes: means for coupling a portion of the laser lightto the interferometer; means for converting an interference fringesignal from the interferometer into a digital signal corresponding tothe interference pattern data, the digital signal being a sampled formof the interference fringe signal; means for estimating the laser phasebased upon the digital signal.
 15. The apparatus in claim 14, furthercomprising: means for estimating a first derivative of the laser opticalphase based in the digital signal including: means for Fouriertransforming the digital signal; means for windowing the transformedsignal to identify a portion of the transformed signal that correspondsto the given optical path delay; means for inverse Fourier transformingthe windowed signal; and means for computing the phase of the signal.16. The apparatus in claim 15, further comprising: means for estimatinga second derivative of the laser optical phase based upon the digitalsignals by identifying zero crossings of the digital signal, and meansfor counting a number of samples between the zero crossings of thedigital signal.
 17. The method in claim 16, wherein the means forcalculating an expected complex response for the given optical pathbased on the estimated laser optical phase further comprises: means forestimating a delayed version of the second derivative of the laseroptical phase; means for calculating a running sum of the secondderivative of the laser optical phase, where a length of the running sumis associated with a length of the given optical path delay; means foraccumulating the running sum; means for calculating a sine of theaccumulated sum to form the imaginary part of the expected complexresponse; and means for calculating a cosine of the accumulated sum toform the real part of the expected complex response.
 18. The apparatusin claim 17, further comprising: means for low pass filtering anddecimating the real and imaginary parts of the expected complex responseto extract interference pattern data associated with the given opticalpath from the interference pattern data generated by the interferometer.19. The apparatus in claim 10, wherein the means are implemented using afield programmable gate array.
 20. The apparatus in claim 10, whereinthe means are implemented using a software programmed data processor.